Training reinforcement learning neural networks

ABSTRACT

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for training a Q network used to select actions to be performed by an agent interacting with an environment. One of the methods includes obtaining a plurality of experience tuples and training the Q network on each of the experience tuples using the Q network and a target Q network that is identical to the Q network but with the current values of the parameters of the target Q network being different from the current values of the parameters of the Q network.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Application No.62/217,547, filed on Sep. 11, 2015. The disclosure of the priorapplication is considered part of and is incorporated by reference inthe disclosure of this application.

BACKGROUND

This specification relates to selecting actions to be performed by areinforcement learning agent.

Reinforcement learning agents interact with an environment by receivingan observation that characterizes the current state of the environmentand, in response, performing an action. Some reinforcement learningagents use neural networks to select the action to be performed inresponse to receiving any given observation.

Neural networks are machine learning models that employ one or morelayers of nonlinear units to predict an output for a received input.Some neural networks are deep neural networks that include one or morehidden layers in addition to an output layer. The output of each hiddenlayer is used as input to the next layer in the network, i.e., the nexthidden layer or the output layer. Each layer of the network generates anoutput from a received input in accordance with current values of arespective set of parameters.

SUMMARY

This specification describes technologies that relate to reinforcementlearning. In general, this specification describes training a Q networkthat is used to select actions to be performed by an agent thatinteracts with an environment by receiving an observation characterizinga current state of the environment and performing an action from a setof actions in response to the observation.

The subject matter described in this specification can be implemented inparticular embodiments so as to realize one or more of the followingadvantages. A reinforcement learning system can effectively learn aneffective action selection policy for an agent by training a Q networkas described in this specification. In particular, by, during thetraining, selecting a next action using the Q network and thendetermining an estimated future cumulative reward for the next actionusing the target Q network, the reinforcement learning system caneffectively learn an action selection policy that avoids overestimatingcumulative future rewards for actions, as can occur when using only thetarget Q network to estimate the future cumulative reward for the nextaction during training. Employing an action selection policy that avoidsoverestimating cumulative rewards can result in the agent achievingimproved performance on a variety of reinforcement learning tasks.

The details of one or more embodiments of the subject matter of thisspecification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example reinforcement learning system.

FIG. 2 is a flow diagram of an example process for adding an experiencetuple to a replay memory.

FIG. 3 is a flow diagram of an example process for updating the currentvalues of the parameters of the Q network.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

This specification generally describes a reinforcement learning systemthat selects actions to be performed by a reinforcement learning agentinteracting with an environment. In order for the agent to interact withthe environment, the system receives data characterizing the currentstate of the environment and selects an action from a set of actionsspace to be performed by the agent in response to the received data.Data characterizing a state of the environment will be referred to inthis specification as an observation.

In some implementations, the environment is a simulated environment andthe agent is implemented as one or more computer programs interactingwith the simulated environment. For example, the simulated environmentmay be a video game and the agent may be a simulated user playing thevideo game. As another example, the simulated environment may be amotion simulation environment, e.g., a driving simulation or a flightsimulation, and the agent is a simulated vehicle navigating through themotion simulation. In these implementations, the actions may be controlinputs to control the simulated user or simulated vehicle.

In some other implementations, the environment is a real-worldenvironment and the agent is a mechanical agent interacting with thereal-world environment. For example, the agent may be a robotinteracting with the environment to accomplish a specific task. Asanother example, the agent may be an autonomous or semi-autonomousvehicle navigating through the environment. In these implementations,the actions may be control inputs to control the robot or the autonomousvehicle.

In some cases, the observations characterize states of the environmentusing low-dimensional feature vectors that characterize the state of theenvironment.

In some other cases, the observations characterize states of theenvironment using high-dimensional pixel inputs from one or more imagesthat characterize the state of the environment, e.g., images of thesimulated environment or images captured by sensors of the mechanicalagent as it interacts with the real-world environment.

FIG. 1 shows an example reinforcement learning system 100. Thereinforcement learning system 100 is an example of a system implementedas computer programs on one or more computers in one or more locationsin which the systems, components, and techniques described below areimplemented.

The reinforcement learning system 100 selects actions to be performed bya reinforcement learning agent 102 interacting with an environment 104.That is, the reinforcement learning system 100 receives observations,with each observation characterizing a respective state of theenvironment 104, and, in response to each observation, selects an actionfrom a set of actions to be performed by the reinforcement learningagent 102 in response to the observation.

In particular, the reinforcement learning system 100 selects actionsusing a Q network 110. The Q network 110 is a deep neural network thatis configured to receive as input an input observation and an inputaction and to generate an estimated future cumulative reward from theinput in accordance with a set of parameters.

The estimated future cumulative reward is an estimate of the futurecumulative reward received if the agent performs the input action inresponse to the input observation. Each reward is a numeric valuereceived, e.g., from the environment, as a consequence of the agentperforming an action and the future cumulated reward is a combination offuture rewards that will be received by the agent after receiving theinput observation. For example, the estimated future cumulative rewardcan be an estimate of time-discounted total future rewards receivedafter the agent performs the action.

To allow the agent 102 to effectively interact with the environment 104,the reinforcement learning system 100 trains the Q network 110 todetermine trained values of the parameters of the Q network 110.

Once the Q network 110 has been trained, the reinforcement learningsystem 100 can effectively use the Q network 110 to select actions to beperformed by the agent 104. In particular, when an observation isreceived after the Q network 110 has been trained, the reinforcementlearning system 100 can, for each action in the set of actions, processthe observation and the action using the Q network 110 in accordancewith the trained values of the parameters of the Q network 110 togenerate a respective estimated future cumulative reward for each of theactions. The reinforcement learning system 100 can then select theaction having the highest estimated future cumulative reward as theaction to be performed by the agent 102 in response to the observation.The agent 102 can then perform the selected action.

In some implementations, the reinforcement learning system 100 can storeor transmit the trained values of the parameters that define the trainedQ network 110 for future use in selection of actions to be performed bythe agent 102 or by another agent.

To assist in the training of the Q network 110, the reinforcementlearning system 100 maintains training components 120 that include areplay memory 130 and a target Q network 150.

The replay memory 130 stores experience tuples generated as aconsequence of the interaction of the agent 102 with the environment 104for use in training the Q network 110.

In particular, each experience tuple in the replay memory includes atraining observation that characterizes a training state of theenvironment, a training action performed by the agent 102 in response tothe training observation, a training reward received by thereinforcement learning system 100 in response to the agent 102performing the training action, and a next observation characterizing anext state of the environment 104, i.e., the state that the environment104 transitioned into after the agent 102 performed the training action.

The reinforcement learning system 100 generates the experience tuplesfrom the interactions of the agent 102 with the environment 104 duringthe training of the Q network 110. An example process for generating anexperience tuple during training is described in more detail below withreference to FIG. 2.

The target Q network 150 is a neural network that is identical to, i.e.,has the same neural network architecture as, the Q network 110, but thathas possibly different parameter values from those of the Q network 110.That is, during the training of the Q network 110, the values of theparameters of the target Q network 150 are only periodically synchedwith the current values of the parameters of the Q network 110.

To train the Q network 110 using the training components 120, thereinforcement learning system 100 repeatedly selects minibatches ofexperience tuples from the replay memory 130. Each minibatch ofexperience tuples includes a predetermined number of experience tuplesand the reinforcement learning system 100 may select the experiencetuples for a given minibatch in any appropriate manner, e.g., randomlyor according to some predetermined criteria.

For each experience tuple in a given minibatch, the reinforcementlearning system 100 uses the Q network 110 and the target Q network 150to determine updates for the current values of the parameters of the Qnetwork 110 and then adjusts the current values of the parameters of theQ network 110 using the updates. Generating these updates and adjustingthe current values of the parameters of the Q network 110 will bedescribed in more detail below with reference to FIG. 3.

During the training, the reinforcement learning system 100 alsoperiodically updates the values of the parameters of the target Qnetwork 150 to match the values of the parameters of the Q network 110.

Once a minibatch of experience tuples has been used in training, thereinforcement learning system 100 can remove the experience tuples inthe minibatch from the replay memory 130.

Generally, during the training, the reinforcement learning system 100generates experience tuples and adds the generated tuples to the replaymemory 130 independently of, i.e., asynchronously from, samplingexperience tuples from the replay memory 130 and adjusting theparameters of the Q network 110.

FIG. 2 is a flow diagram of an example process 200 for adding anexperience tuple to a replay memory. For convenience, the process 200will be described as being performed by a system of one or morecomputers located in one or more locations. For example, a reinforcementlearning system, e.g., the reinforcement learning system 100 of FIG. 1,appropriately programmed in accordance with this specification, canperform the process 200.

The system receives a current observation characterizing the currentstate of the environment (step 202).

For each action in the set of actions, the system processes the currentobservation and the action using the Q network in accordance withcurrent values of the parameters of the Q network (step 204). Asdescribed above, the Q network is a deep neural network that isconfigured to receive as input an observation and an action and togenerate an estimated future cumulative reward from the input inaccordance with a set of parameters. Thus, by, for each action,processing the current observation and the action using a Q network inaccordance with current values of the parameters of the Q network, thesystem generates a respective estimated future cumulative reward foreach action in the set of actions.

The system selects an action to be performed by the agent in response tothe current observation using the estimated future cumulative rewards(step 206).

In some implementations, the system selects the action with the highestestimated cumulative future reward as the action to be performed by theagent.

In some other implementations, to encourage exploration of theenvironment during training, the system selects the action using anexploration policy, e.g., by selecting the action with the highestestimated cumulative future with probability 1−ε and randomly selectingan action from the set with probability ε.

The system receives a reward and a next observation (step 206). The nextobservation characterizes the next state of the environment, i.e., thestate that the environment transitioned into as a result of the agentperforming the selected action, and the reward is a numeric value thatis received by the system, e.g., from the environment, as a consequenceof the agent performing the selected action.

The system generates an experience tuple that includes the currentobservation, the selected action, the reward, and the next observationand stores the generated experience tuple in a replay memory for use intraining the Q network (step 208).

FIG. 3 is a flow diagram of an example process 300 for determining anupdate to the current values of the parameters of the Q network. Forconvenience, the process 300 will be described as being performed by asystem of one or more computers located in one or more locations. Forexample, a reinforcement learning system, e.g., the reinforcementlearning system 100 of FIG. 1, appropriately programmed in accordancewith this specification, can perform the process 300.

The system receives an experience tuple (step 302). The experience tupleis one of the experience tuples in a minibatch of experience tuplessampled from the replay memory by the system.

The experience tuple includes a training observation characterizing atraining state of the environment, a training action from the set ofactions that was performed by the agent in response to receiving thetraining observation, a training reward received as a consequence of theagent performing the training action, and a next training observationcharacterizing a next training state of the environment.

The system processes the training observation and the training action inthe experience tuple using the Q network to determine a currentestimated future cumulative reward for the experience tuple inaccordance with current values of the parameters of the Q network (step304).

The system selects a next action from the set of actions (step 306). Thenext action is the action that, when processed in combination with thenext observation by the Q network, generates the highest estimatedfuture cumulative reward. That is, for each action in the set ofactions, the system processes the next observation and the action usingthe Q network in accordance with the current values of the parameters ofthe Q network to generate a next estimated future cumulative reward forthe action. The system then selects the action having the highest nextestimated future cumulative reward as the next action.

The system processes the next observation and the next action using thetarget Q network to generate a next target estimated future cumulativereward for the next action in accordance with current values of theparameters of the target Q network (step 308). As described above, thetarget Q network is identical to the Q network but the current values ofthe parameters of the target Q network are generally different from thecurrent values of the parameters of the Q network.

Thus, to determine the next target estimated future cumulative rewardfor the experience tuple, the system uses the Q network to select thenext action and then uses the target Q network to generate the nexttarget estimated future cumulative reward instead of directly using thelargest target estimated future cumulative reward generated by thetarget Q network as the next target estimated future cumulative reward.

The system determines an error for the experience tuple from the currentestimated future reward, the training reward, and the next targetestimated future cumulative reward (step 310). For example, the error Emay satisfy:

E=R+γ*NTER−CER,

where R is the reward in the experience tuple, γ is a specified discountfactor, NTER is the next target estimated future cumulative reward, andCER is the current estimated future cumulative reward.

The system uses the error to update the current values of the parametersof the Q network (step 312). That is, the system can determine an updateto the current values of the parameters of the Q network that reducesthe error using conventional machine learning training techniques, e.g.,by performing an iteration of gradient descent with backpropagation.Once an update for each experience tuple in the minibatch has beendetermined, the system can apply the updates to the current values ofthe parameters of the Q network to generate updated values of theparameters.

Once updated values of the parameters of Q network have been determined,the system determines whether criteria for updating the current valuesof the target Q network parameters are satisfied. For example, thesystem may update the parameters of the target Q network after every Tminibatches have been processed, with T being an integer greater than 1.

If the criteria are satisfied, the system updates the current values ofthe target Q network parameters to synchronize them with the updatedvalues of the Q network parameters.

By repeatedly performing the process 300 on multiple differentminibatches of experience tuples, the system can train the Q network todetermine trained values of the parameters of the Q network and to allowthe Q network to effectively be used to select actions to be performedby the agent in interacting with the environment. In particular, byusing the Q network to select the next action and then using the targetQ network to generate the next target estimated future cumulative rewardinstead of directly using the largest target estimated future cumulativereward generated by the target Q network as the next target estimatedfuture cumulative reward during the training, the system can mitigateoverestimation errors in the estimated rewards generated by the trainedQ network.

For a system of one or more computers to be configured to performparticular operations or actions means that the system has installed onit software, firmware, hardware, or a combination of them that inoperation cause the system to perform the operations or actions. For oneor more computer programs to be configured to perform particularoperations or actions means that the one or more programs includeinstructions that, when executed by data processing apparatus, cause theapparatus to perform the operations or actions.

Embodiments of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly-embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Embodiments of the subject matter described in thisspecification can be implemented as one or more computer programs, i.e.,one or more modules of computer program instructions encoded on atangible non-transitory program carrier for execution by, or to controlthe operation of, data processing apparatus. Alternatively or inaddition, the program instructions can be encoded on anartificially-generated propagated signal, e.g., a machine-generatedelectrical, optical, or electromagnetic signal, that is generated toencode information for transmission to suitable receiver apparatus forexecution by a data processing apparatus. The computer storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofone or more of them.

The term “data processing apparatus” refers to data processing hardwareand encompasses all kinds of apparatus, devices, and machines forprocessing data, including by way of example a programmable processor, acomputer, or multiple processors or computers. The apparatus can also beor further include special purpose logic circuitry, e.g., an FPGA (fieldprogrammable gate array) or an ASIC (application-specific integratedcircuit). The apparatus can optionally include, in addition to hardware,code that creates an execution environment for computer programs, e.g.,code that constitutes processor firmware, a protocol stack, a databasemanagement system, an operating system, or a combination of one or moreof them.

A computer program (which may also be referred to or described as aprogram, software, a software application, a module, a software module,a script, or code) can be written in any form of programming language,including compiled or interpreted languages, or declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A computer program may, butneed not, correspond to a file in a file system. A program can be storedin a portion of a file that holds other programs or data, e.g., one ormore scripts stored in a markup language document, in a single filededicated to the program in question, or in multiple coordinated files,e.g., files that store one or more modules, sub-programs, or portions ofcode. A computer program can be deployed to be executed on one computeror on multiple computers that are located at one site or distributedacross multiple sites and interconnected by a communication network.

The processes and logic flows described in this specification can beperformed by one or more programmable computers executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application-specific integrated circuit).

Computers suitable for the execution of a computer program include, byway of example, can be based on general or special purposemicroprocessors or both, or any other kind of central processing unit.Generally, a central processing unit will receive instructions and datafrom a read-only memory or a random access memory or both. The essentialelements of a computer are a central processing unit for performing orexecuting instructions and one or more memory devices for storinginstructions and data. Generally, a computer will also include, or beoperatively coupled to receive data from or transfer data to, or both,one or more mass storage devices for storing data, e.g., magnetic,magneto-optical disks, or optical disks. However, a computer need nothave such devices. Moreover, a computer can be embedded in anotherdevice, e.g., a mobile telephone, a personal digital assistant (PDA), amobile audio or video player, a game console, a Global PositioningSystem (GPS) receiver, or a portable storage device, e.g., a universalserial bus (USB) flash drive, to name just a few.

Computer-readable media suitable for storing computer programinstructions and data include all forms of non-volatile memory, mediaand memory devices, including by way of example semiconductor memorydevices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks,e.g., internal hard disks or removable disks; magneto-optical disks; andCD-ROM and DVD-ROM disks. The processor and the memory can besupplemented by, or incorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube) or LCD (liquidcrystal display) monitor, for displaying information to the user and akeyboard and a pointing device, e.g., a mouse or a trackball, by whichthe user can provide input to the computer. Other kinds of devices canbe used to provide for interaction with a user as well; for example,feedback provided to the user can be any form of sensory feedback, e.g.,visual feedback, auditory feedback, or tactile feedback; and input fromthe user can be received in any form, including acoustic, speech, ortactile input. In addition, a computer can interact with a user bysending documents to and receiving documents from a device that is usedby the user; for example, by sending web pages to a web browser on auser's client device in response to requests received from the webbrowser.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back-end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front-end component, e.g., aclient computer having a relationship graphical user interface or a Webbrowser through which a user can interact with an implementation of thesubject matter described in this specification, or any combination ofone or more such back-end, middleware, or front-end components. Thecomponents of the system can be interconnected by any form or medium ofdigital data communication, e.g., a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), e.g., the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or of what may be claimed, but rather as descriptions offeatures that may be specific to particular embodiments of particularinventions. Certain features that are described in this specification inthe context of separate embodiments can also be implemented incombination in a single embodiment. Conversely, various features thatare described in the context of a single embodiment can also beimplemented in multiple embodiments separately or in any suitablesubcombination. Moreover, although features may be described above asacting in certain combinations and even initially claimed as such, oneor more features from a claimed combination can in some cases be excisedfrom the combination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various system modulesand components in the embodiments described above should not beunderstood as requiring such separation in all embodiments, and itshould be understood that the described program components and systemscan generally be integrated together in a single software product orpackaged into multiple software products.

Particular embodiments of the subject matter have been described. Otherembodiments are within the scope of the following claims. For example,the actions recited in the claims can be performed in a different orderand still achieve desirable results. As one example, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In certain implementations, multitasking and parallelprocessing may be advantageous.

What is claimed is:
 1. A method of training a Q network used to selectactions to be performed by an agent that interacts with an environmentby receiving observations characterizing states of the environment andperforming actions from a set of actions in response to theobservations, wherein the Q network is a deep neural network that isconfigured to receive as input an input observation and an input actionand to generate an estimated future cumulative reward from the input inaccordance with a set of parameters, and wherein the method comprises:obtaining a plurality of experience tuples, wherein each experiencetuple includes a training observation, an action performed by the agentin response to receiving the training observation, a reward received inresponse to the agent performing the action, and a next trainingobservation that characterizes a next state of the environment; andtraining the Q network on each of the experience tuples, comprising, foreach experience tuple: processing the training observation in theexperience tuple and the action in the experience tuple using the Qnetwork to determine a current estimated future cumulative reward forthe experience tuple in accordance with current values of the parametersof the Q network; selecting an action from the set of actions that, whenprocessed in combination with the next observation by the Q network,results in the Q network generating a highest estimated futurecumulative reward; processing the next observation in the experiencetuple and the selected action using a target Q network to determine anext target estimated future cumulative reward for the selected actionin accordance with current values of the parameters of the target Qnetwork, wherein the target Q network is identical to the Q network butthe current values of the parameters of the target Q network aredifferent from the current values of the parameters of the Q network;determining an error for the experience tuple from the reward in theexperience tuple, the next target estimated future cumulative reward forthe selected action, and the current estimated future cumulative reward;and using the error for the experience tuple to update the currentvalues of the parameters of the Q network.
 2. The method of claim 1,wherein the error E satisfies:E=R+γ*NTER−CER, where R is the reward in the experience tuple, γ is aspecified discount factor, NTER is the next target estimated futurecumulative reward for the selected action, and CER is the currentestimated future cumulative reward.
 3. The method of claim 1, whereinusing the error for the experience tuple to update the current values ofthe parameters of the Q network comprises: updating the current valuesof the parameters of the Q network to reduce the error using a machinelearning training technique.
 4. The method of claim 1, wherein selectingthe action comprises: for each action in the set of actions, processingthe next observation in the experience tuple and the action using the Qnetwork to determine a respective next estimated future cumulativereward for the action in accordance with current values of theparameters of the Q network; and selecting the action having the highestnext estimated future cumulative reward.
 5. The method of claim 1,wherein the values of the parameters of the target Q network areperiodically synchronized with the values of the parameters of the Qnetwork.
 6. The method of claim 5, further comprising: after trainingthe Q network on each of the experience tuples to determine updatedvalues of the parameters of the Q network, updating the current valuesof the target Q network to match the updated values of the parameters ofthe Q network.
 7. A system comprising one or more computers and one ormore storage devices storing instructions that, when executed by the oneor more computers, cause the one or more computers to perform operationsfor training a Q network used to select actions to be performed by anagent that interacts with an environment by receiving observationscharacterizing states of the environment and performing actions from aset of actions in response to the observations, wherein the Q network isa deep neural network that is configured to receive as input an inputobservation and an input action and to generate an estimated futurecumulative reward from the input in accordance with a set of parameters,and wherein the operations comprise: obtaining a plurality of experiencetuples, wherein each experience tuple includes a training observation,an action performed by the agent in response to receiving the trainingobservation, a reward received in response to the agent performing theaction, and a next training observation that characterizes a next stateof the environment; and training the Q network on each of the experiencetuples, comprising, for each experience tuple: processing the trainingobservation in the experience tuple and the action in the experiencetuple using the Q network to determine a current estimated futurecumulative reward for the experience tuple in accordance with currentvalues of the parameters of the Q network; selecting an action from theset of actions that, when processed in combination with the nextobservation by the Q network, results in the Q network generating ahighest estimated future cumulative reward; processing the nextobservation in the experience tuple and the selected action using atarget Q network to determine a next target estimated future cumulativereward for the selected action in accordance with current values of theparameters of the target Q network, wherein the target Q network isidentical to the Q network but the current values of the parameters ofthe target Q network are different from the current values of theparameters of the Q network; determining an error for the experiencetuple from the reward in the experience tuple, the next target estimatedfuture cumulative reward for the selected action, and the currentestimated future cumulative reward; and using the error for theexperience tuple to update the current values of the parameters of the Qnetwork.
 8. The system of claim 7, wherein the error E satisfies:E=R+γ*NTER−CER, where R is the reward in the experience tuple, γ is aspecified discount factor, NTER is the next target estimated futurecumulative reward for the selected action, and CER is the currentestimated future cumulative reward.
 9. The system of claim 7, whereinusing the error for the experience tuple to update the current values ofthe parameters of the Q network comprises: updating the current valuesof the parameters of the Q network to reduce the error using a machinelearning training technique.
 10. The system of claim 7, whereinselecting the action comprises: for each action in the set of actions,processing the next observation in the experience tuple and the actionusing the Q network to determine a respective next estimated futurecumulative reward for the action in accordance with current values ofthe parameters of the Q network; and selecting the action having thehighest next estimated future cumulative reward.
 11. The system of claim7, wherein the values of the parameters of the target Q network areperiodically synchronized with the values of the parameters of the Qnetwork.
 12. The system of claim 11, the operations further comprising:after training the Q network on each of the experience tuples todetermine updated values of the parameters of the Q network, updatingthe current values of the target Q network to match the updated valuesof the parameters of the Q network.
 13. One or more non-transitorycomputer storage media encoded with instructions that, when executed byone or more computers, cause the one or more computers to performoperations for training a Q network used to select actions to beperformed by an agent that interacts with an environment by receivingobservations characterizing states of the environment and performingactions from a set of actions in response to the observations, whereinthe Q network is a deep neural network that is configured to receive asinput an input observation and an input action and to generate anestimated future cumulative reward from the input in accordance with aset of parameters, and wherein the operations comprise: obtaining aplurality of experience tuples, wherein each experience tuple includes atraining observation, an action performed by the agent in response toreceiving the training observation, a reward received in response to theagent performing the action, and a next training observation thatcharacterizes a next state of the environment; and training the Qnetwork on each of the experience tuples, comprising, for eachexperience tuple: processing the training observation in the experiencetuple and the action in the experience tuple using the Q network todetermine a current estimated future cumulative reward for theexperience tuple in accordance with current values of the parameters ofthe Q network; selecting an action from the set of actions that, whenprocessed in combination with the next observation by the Q network,results in the Q network generating a highest estimated futurecumulative reward; processing the next observation in the experiencetuple and the selected action using a target Q network to determine anext target estimated future cumulative reward for the selected actionin accordance with current values of the parameters of the target Qnetwork, wherein the target Q network is identical to the Q network butthe current values of the parameters of the target Q network aredifferent from the current values of the parameters of the Q network;determining an error for the experience tuple from the reward in theexperience tuple, the next target estimated future cumulative reward forthe selected action, and the current estimated future cumulative reward;and using the error for the experience tuple to update the currentvalues of the parameters of the Q network.
 14. The computer storagemedia of claim 13, wherein the error E satisfies:E=R+γ*NTER−CER, where R is the reward in the experience tuple, γ is aspecified discount factor, NTER is the next target estimated futurecumulative reward for the selected action, and CER is the currentestimated future cumulative reward.
 15. The computer storage media ofclaim 13, wherein using the error for the experience tuple to update thecurrent values of the parameters of the Q network comprises: updatingthe current values of the parameters of the Q network to reduce theerror using a machine learning training technique.
 16. The computerstorage media of claim 13, wherein selecting the action comprises: foreach action in the set of actions, processing the next observation inthe experience tuple and the action using the Q network to determine arespective next estimated future cumulative reward for the action inaccordance with current values of the parameters of the Q network; andselecting the action having the highest next estimated future cumulativereward.
 17. The computer storage media of claim 13, wherein the valuesof the parameters of the target Q network are periodically synchronizedwith the values of the parameters of the Q network.
 18. The computerstorage media of claim 17, the operations further comprising: aftertraining the Q network on each of the experience tuples to determineupdated values of the parameters of the Q network, updating the currentvalues of the target Q network to match the updated values of theparameters of the Q network.